Chapter 7, Problem 3RP

To determine

To prove : The congruency of $\angle BDC\cong \angle FDE$

Explanation of Solution

Given information : The following information has been given

  $\overrightarrow{AC}\cong \overrightarrow{AE}$

  $\angle CBD\cong \angle EFD$

Formula used : The sum of the angles of any triangle add up to ${180}^0$

Proof : We know that $\overrightarrow{AC}\cong \overrightarrow{AE}$ , hence we can say that in triangles CBD and EFD,

  $\angle BCD\cong \angle FED$

Also, $\angle CBD\cong \angle EFD$ is given

Thus, we know that the sum of the angles in any triangle will remain constant. Hence, we can say that the remaining angle in in triangles CBD and EFD will also be congruent

Thus, $\angle BDC\cong \angle FDE$